Harvey Keitel talking about being fired from Eyes Wide Shut
One of the reasons Kubrick had to do so many takes is because he needed very precise alignments with actors and symbols in the scene. Here's one well known example from Eyes Wide Shut. It takes time to get this kind of double precision in one tracking shot, especially when you're not telling the actors about the alignment you're looking for because it's part of a closely held symbolic puzzle.
It’s exactly the opposite to what you say: the more precise, the less secret something is on set by necessity. Most of EWS is shot on Steadicam primarily by Elizabeth Ziegler and Peter Cavaciutu, and we know from reports from technicians (Team Deakins podcast for example) that worked on the show and from Leon Vitali that he was very explicit with his camera instructions using marks and even laser pointers on the steadicam rig at times, to triangulate exact framings (you can see this in BTS shots of the orgy set) which everyone can see on the monitors. The actors and operators quickly learn. There’s no such thing as a ‘secret framing’ on set, let-alone on a Kubrick set where things are so precise.
